A185664 Riordan array (A000045(x)^m,x*A000108(x)), m=3.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 0, 9, 4, 1, 0, 0, 0, 22, 14, 5, 1, 0, 0, 0, 51, 42, 20, 6, 1, 0, 0, 0, 111, 120, 69, 27, 7, 1, 0, 0, 0, 233, 335, 224, 104, 35, 8, 1, 0, 0, 0, 474, 940, 707, 372, 148, 44, 9, 1, 0, 0, 0, 942, 2695, 2221, 1281, 574, 202, 54, 10, 1, 0, 0, 0, 1836, 7980, 7038, 4343, 2122, 841, 267, 65, 11, 1, 0, 0, 0

Offset

0,11

Links

Table of n, a(n) for n=0..90.

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

R(n,k,m)=k*sum(i=0..n-k, sum(j=ceiling((i-m)/2)..i-m, binomial(j,i-m-j)*binomial(m+j-1,m-1))*binomial(2*(n-i)-k-1,n-i-1)/(n-i)), k>0.

R(n,0,m)=sum(j=ceiling((i-m)/2)..n-m, binomial(j,n-m-j)*binomial(m+j-1,m-1)), m=3.

Example

0;
0,0;
0,0,0;
1,0,0,0;
3,1,0,0,0;
9,4,1,0,0,0;
22,14,5,1,0,0,0;
51,42,20,6,1,0,0,0;

Crossrefs

Cf. A001628 (column k=0).

Sequence in context: A128208 A154721 A350449 * A300812 A144209 A094544

Adjacent sequences: A185661 A185662 A185663 * A185665 A185666 A185667

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 08 2011

Status

approved